sure its possible, here are the steps i would do:
sql table
ID|plaeruniqueid|name|score|
phpapi
- requests scores
- submit scores
html5game
- generates a unique id (for example a big random value) and saves it in local storrage at the first start
- makes a ajax request to submit thi highscore (maybe automatically) api
- makes a ajaxrequest to get the highscore to the php api
I am sure there is an example somewhere. Look arround a little. also you can modify the login examples to your need and replace the login with the unique id.
this way is not very secure but it will suit your needs.
you could work with encryption to make it a little more secure (generation and transfer)
kind regards